Orientation reversal of manifolds

Abstract

We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self map of degree -1. We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension ≥ 3. We also produce simplyconnected, strongly chiral manifolds in every dimension ≥ 7. For every k ≥ 1, we exhibit lens spaces with an orientation reversing self diffeomorphism of order 2k but no selfmap of degree -1 of smaller order. © 2009 Mathematical Sciences Publishers.